Graduate Aptitude Test in Engineering 2017

Question Paper Name: Computer Science and Information Technology 11th Feb 2017 Session 1

Subject Name: Computer Science and Information Technology

Duration : 180

Total Marks: 100

1. Let X be a Gaussian random variable mean 0 and variance σ². Let Y=max(X, 0) where max (a,b) is the maximum of a and b. The median of Y is ____________.

Ans: (0)

2. Consider the Karnaugh map given below, where x represents “don’t care” and blank represents 0.

Assume for all inputs (a, b, c, d) the respective complements are also available. The above logic is implemented 2-input NOR gates only. The minimum number of gates required is ____________.

Ans: (1)

3. The statement (¬p) ⇒ (¬q) is logically equivalent to which of the statements below?

I. p ⇒ q

II. q ⇒ p

III. (¬q) ⋁ p

(¬p) ⋁ q

(A) I only

(B) I and IV only

(D) II and III only

Ans: (D)

4. Consider the following table:

Match the algorithms to the design paradigms they are based on.

(A) P-(ii), Q-(iii),R-(i)

(B) P-(iii), Q-(i), R-(ii)

(D) P-(i), Q-(ii), R-(iii)

Ans: (C)

5. A sender S sends a message m to receiver R, which is digitally signed by S with its private key. In this scenario, one or more of the following security violations can take place.

I. S can launch a birthday attack to replace m with a fraudulent message.

II. A third party attacker can launch a birthday attack to replace m with a fraudulent message.

III. R can launch a birthday attack to replace m with a fraudulent message.

Which of the following are possible security violations?

(A) I and II only

(B) I only

(D) II and III only

Ans: (B)

6. Consider the following grammar.

What is FOLLOW (Q) ?

(A) {R}

(B) {w}

(D) {w, $}

Ans: (C)

7. Consider the language L given by the regular expression (a + b)^*b(a + b) over the alphabet {a, b}. The smallest number of states needed in a deterministic finite-state automation (DFA) accepting L is ___________.

Ans: (4)

8. Consider a two-level cache hierarchy with L1 and L2 caches. An application incurs 1.4 memory accesses per instruction on average. For this application, the miss rate of L1 cache 0.1, the L2 cache experiences, on average, 7 misses per 1000 instructions. The miss rate of L2 expressed correct to two decimal places is ___________.

Ans: (0.05)

9. Consider the following CPU processes with arrival times (in milliseconds) and length of CPU burst (in milliseconds) as given below:

If the pre-emptive shortest remaining time first scheduling algorithm is used to schedule the processes., then the average waiting time across all processes is ________ milliseconds.

Ans: (3)

10. Threads of a process share

(A) global variable but not heap.

(B) heap but not global variables.

(D) Both heap and global variables.

Ans: (D)

11. Let c₁ …… c_n be scalars, not all zero, such that where a_i are column vectors in Rⁿ. Consider the set of linear equations Ax = b

where A = [a_i……..a_n] and The set of equations has

(A) a unique solution at x = J_n where J_n denotes a n-dimensional vector of all 1

(B) no solution

(D) finitely many solutions.

Ans: (C)

12. Consider the C code fragment given below.

Assuming that m and n point to valid NULL- terminated linked lists, invocation of join will

(A) append list m to the end of list n for all inputs.

(B) either cause a null pointer dereference or append list m to the end of list n.

(D) append list n to the end of list m for all inputs.

Ans: (B)

13. The n-bit fixed-point representation of an unsigned real number real X uses f bits for the fraction part. Let i = n –f. The range of decimal values for X in this representation is

(A) 2⁻^f to 2ⁱ

(B) 2⁻^f to (2ⁱ – 2⁻^f)

(D) 0 to (2ⁱ – 2⁻^f)

Ans: (D)

14. Consider the following intermediate program in three address code

p = a− b

q = p *c

p = u * v

q = p + q

Which one of the following corresponds to a static single assignment form of the above code?

(A)

(B)

(C)

(D)

Ans: (B)

15. Consider the C struct defined below:

struct data {

int marks [100] ;

char grade;

int cnumber;

};

struct data student;

The base address of student is available in register R1. The field student.grade can be accessed efficiently using

(A) Post-increment addressing mode. (R1)+

(B) Pre-decrement addressing mode, -(R1)

(D) Index addressing mode, X(R1), where X is an offset represented in 2’s complement 16-bit representation.

Ans: (D)

16. Consider a TCP client and a TCP server running on two different machines. After completing data transfer, the TCP client calls close to terminate the connectional and a FIN segment is sent to the TCP server. Server-side TCP responds by sending an ACK which is received by the client-side TCP. As per the TCP connections state diagram (RFC 793), in which state does the client-side TCP connection wait for the FIN from the sever-side TCP?

(A) LAST-ACK

(B) TIME-WAIT

(D) FIN-WAIT-2

Ans: (D)

17. Consider the following context-free grammar over the alphabet ∑ = {a,b,c} with S as the start symbol.

S → abScT|abc T

T → bT|b

Which one of the following represents the language generated by the above grammar ?

(A) {(ab)ⁿ (cb)ⁿ | n ≥ 1}

(B)

(D) {(ab)ⁿ (cbⁿ)^m| m, n ≥ 1

Ans: (B)

18. Consider the first-order logic sentence F : ∀ z(∃yR (x, y)). Assuming non-empty logical domains, which of the sentences below are implied by F?

I. ∃y(∃xR(x, y)) II. ∃y(∀xR(x, y))

III. ∀y(∃xR (x, y)) IV. ¬∃x(∀y¬R(x, y))

(A) IV only

(B) I and IV only

(D) II and III only

Ans: (B)

19. When two 8-bit numbers A₇…..A₀ and B₇…..B₀ in 2’s complement representation (with A₀ and B₀ as the least significant bits ) are added using a ripple-carry adder, the sum bits obtained are S₇……S₀ and the carry bits are C₇….C₀. An overflow is said to have occurred if

(A) the carry bit C₇ is 1

(B) all the carry bits (C₇….C₀) are 1

(C)

(D)

Ans: (C)

20. Consider a database that has the relation schema EMP (EmpId, EmpName, and DeptName). An instance of the schema EMP and a SQL query on it are given below.

The output of executing the SQL query is _____.

Ans: (2.6)

21. The following functional dependencies hold true for the relational schema R{V,W,X,Y,Z}:

Which of the following is irreducible equivalent for this set of functional dependencies ?

(A)

(B)

(C)

(D)

Ans: (A)

22. Consider the following functions from positive integers to real numbers:

The CORRECT arrangement of the above functions in increasing order of asymptotic complexity is:

(A)

(B)

(C)

(D)

Ans: (B)

23. Let T be a tree with 10 vertices. The sum of the degrees of all the vertices in T is _________.

Ans: (18)

24. Let T be a binary search tree with 15 nodes. The minimum and maximum possible heights of T are :

Note: The height of a tree with a single node is 0.

(A) 4 and 15 respectively

(B) 3 and 14 respectively

(D) 3 and 15 respectively

Ans: (B)

25. Consider the following C code:

# include <stdio.h>

int * assignval (int *x, int val) {

*x = val;

return x;

}

void main ( ) {

int * x= malloc (sizeof (int));

if (NULL = = x) return;

x = assignval (x,0);

if(x) {

x=(int *) malloc (sizeof (int));

if (NULL = = x) return;

x = assignval (x, 10);

}

printf(“%d\n”, *x);

free (x);

}

The code suffers from which one of the following problems:

(A) compiler error as the return of malloc is not typecast appropriately.

(B) compiler error because the comparison should be made as x==NULL and not as shown.

(D) compiles successfully but execution may result in memory leak.

Ans: (D)

26. Consider a combination of T and D flip-flops connected as shown below. The output of the D flip-flop is connected to the input of the T flip-flop and the output of the T Flip-flop is connected to the input of the D Flip-flop.

Initially, both Q₀ and Q₁ are set to 1 (before the 1^st clock cycle). The outputs

(A) Q₁Q₀ after the 3^rd cycle are 11 and after the 4^th cycle are 00 respectively

(B) Q₁Q₀ after the 3^rd cycle are 11 and after the 4^th cycle are 01 respectively

(D) Q₁Q₀ after the 3^rd cycle are 01 and after the 4^th cycle are 01 respectively

Ans: (B)

27. The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ______________.

Ans: (271)

28. Consider a RISC machine where each instruction is exactly 4 bytes long. Conditional and unconditional branch instructions use PC- relative addressing mode with Offset specified in bytes to the target location of the branch instruction. Further the Offset is always with respect to the address of the next instruction in the program sequence. Consider the following instruction sequence.

Instr. No. Instruction

i: add R2, R3, R4

i + 1; sub R5, R6, R7

i + 2; cmp R1, R9, R10

i + 3 beq R1, Offset

If the target of the branch instruction is i, then the decimal value of the Offset is __________.

Ans: (−16)

29. Consider the C functions foo and bar given below:

int foo (int val ) {

int x = 0;

while (val > 0) {

x = x + foo ( val –);

}

return val ;

}

int bar (int val ) {

int x = 0;

while (val > 0) {

x = x + bar (val – 1) ;

}

return val ;

}

Invocations of foo (3) and bar (3) will result in:

(A) Return of 6 and 6 respectively.

(B) Infinite loop and abnormal termination respectively.

(D) Both terminating abnormally

Ans: (B)

30. In a RSA cryptosystem a participant A uses two prime numbers p = 13 and q =17 to generate her public and private keys. If the public key of A is 35. Then the private key of A is __________.

Ans: (11)

31. Let A be an array of 31 numbers consisting of sequence of 0’s followed by a sequence of 1’s. The problem is to find the smallest index i that A[i] is 1 by probing the minimum numbers of locations in A. The worst case number of probes performed by an optimal algorithm is _____________.

Ans: (5)

32. If G is grammar with productions

S → SaS|aSb|bSa|SS|∈

where S is the start variable, then which one of the following is not generated by G?

(A) abab

(B) aaab

(D) babba

Ans: (D)

33. The value of

(A) is 0

(B) is −1

(D) does not exist

Ans: (C)

34. Instructions execution in a processor is divided into 5 stages. Instruction Fetch (IF), Instruction Decode (ID) , Operand Fetch (OF), Execute (EX), and Write Back (WB), These stages take 5,4,20, 10 and 3 nanoseconds (ns) respectively. A pipelined implementation of the processor requires buffering between each pair of consecutive stages with a delay of 2ns. Two pipelined implementations of the processor are contemplated.

(i) a naïve pipeline implementation (NP) with 5 stages and

(ii) an efficient pipeline (EP) where the OF stage id divided into stages OF1 and OF2 with execution times of 12 ns and 8 ns respectively.

The speedup (correct to two decimals places) achieved by EP over NP in executing 20 independent instructions with no hazards is ________________.

Ans: (1.508)

35. Consider a database that has the relation schemas EMP(EmpId, EmpName, DepId). And DEPT(DeptName, DeptId). Note that the DeptId can be permitted to be NULL in the relation EMP. Consider the following queries on the database expressed in tuple relational calculus.

Which of the above queries are safe?

(A) (I) and (II) only

(B) (I) and (III) only

(D) (I), (II) and (III)

Ans: (D)

36. Recall that Belady’s anomaly is that the pages-fault rate may increase as the number of allocated frames increases. Now consider the following statements:

S1: Random page replacement algorithm (where a page chosen at random is replaced) suffers from Belady’s anomaly

S2: LRU page replacement algorithm suffers from Belady’s anomaly

Which of the following is CORRECT ?

(A) S1 is true, S2 is true

(B) S1 is true, S2 is false

(D) S1 is false, S2 is false

Ans: (B)

37. The output of executing the following C program is ________.

# include <stdio.h>

int total (int v) {

while (v) {

count + = v & 1;

v>> = 1;

}

return count;

}

void main ( ) {

static int x = 0;

int i = 5;

for (; i> 0; i–) {

x=x + total (i) ;

}

printf (“%d\n”, x) ;

}

Ans: (23)

38. Consider the following C program.

#include <stdio.h>

#include<string.h>

void printlength (char *s, char *t) {

unsigned int c = 0;

int len = ((strlen(s) – strlen (t)) > c) ? strlen(s): strlen(t);

printf (“%d\n”, len);

}

void main ( ) {

char *x = “abc”;

char *y =”defgh”;

printlength (x,y);

Recall that strlen is defined in string.h as returning a value of type size_t, which is an unsigned int. The output of the program is _____________.

Ans: (3)

39. Consider the following languages over the alphabet ∑ = {a, b, c}

Let L₁ = {aⁿbⁿc^m|m, n ≥ 0} and L₂ = {a^mbⁿcⁿ|m, n ≥ 0}

Which of the following are context-free languages ?

I. L₁ ⋃ L₂ II. L₁ ⋂ L₂

(A) I only

(B) II only

(D) Neither I nor II

Ans: (A)

40. Consider a 2-way set associative cache with 256 blocks and uses LRU replacement, Initially the cache is empty. Conflict misses are those misses which occur due the contention of multiple blocks for the same cache set. Compulsory misses occur due to first time access to the block. The following sequence of accesses to memory blocks.

(0,128,256,128,0,128,256,128,1,129,257,129,1,129,257,129)

is repeated 10 times. The number of conflict misses experienced by the cache is ___________.

Ans: (76)

41. Let u and v be two vectors in R² whose Euclidean norms satisfy ||u|| = 2||v||. What is the value of α such that w = u + αv bisects the angle between u and v ?

(A) 2

(B) 1/2

(D) −1/2

Ans: (A)

42. Consider the following grammar:

stmt → if exp r then else expr ;stmt|0

expr → termrelop term|term

if → a|b|c

number → [0 – 9]

where relop is a relational operate (e.g <, >,….) —O refers to the empty statement, and if ,then, else are terminals.

Consider a program P following the above grammar containing ten if terminals. The number of control flows paths in P is ____________. For example the program

if e₁ then e₂ else e₃

has 2 controls flow paths e₁ → e₂ and e₁ → e₃

Ans: (1024)

43. In a database system, unique time stamps are assigned to each transaction using Lamport’s logical clock . Let TS(T₁) and TS(T₂) be the timestamps of transactions T₁ and T₂ Besides, T₁ holds a lock on the resource R, and T₂ has requested a conflicting lock on the same resource R. The following algorithm is used to prevent deadlocks in the database system assuming that a killed transaction is restarted with the same timestamp.

if TS(T₂) < TS (T₁) then

T₁ is killed

else T₂ waits.

Assume any transactions that is not killed terminates eventually. Which of the following is TRUE about the database system that uses the above algorithm to prevent deadlocks?

(A) The database system is both deadlock-free and starvation- free.

(B) The database system is deadlock- free, but not starvation-free.

(D) The database system is neither deadlock- free nor starvation-free.

Ans: (A)

44. Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A^* to B^*. We say f is computable if there exists a Turning machine M which given an input x in A^*, always halts with f(x) on its tape. Let L_f denote the language {x#f (x)| x∈A^*} .Which of the following statements is true:

(A) f if computable if and only if L_f is recursive.

(B) f is computable if and only L_f recursively enumerable.

(D) If f is computable then L_f is recursively enumerable, but not conversely.

Ans: (A)

45. Consider the expression (a – 1)^* (((b + c)/3)+d)). Let X be the minimum number of registers required by an optimal code generation (without any register spill) algorithm for a load/store architecture in which (i) only loads and store instructions can have memory operands and (ii) arithmetic instructions can have only register or immediate operands. The value of X is _________.

Ans: (2)

46. Let G = (V, E) be any connected undirected edge-weighted graph. The weights of the edges in E are positive and distinct. Consider the following statements:

(I) Minimum spanning tree of G is always unique.

(II) Shortest path between any two vertices of G is always unique.

Which of the above statements is/are necessarily true?

(A) (I) only

(B) (II) only

(D) Neither (I) nor (II)

Ans: (A)

47. A multithreaded program P executes with x number of threads and uses y number of locks for ensuring mutual exclusion while operating on shared memory locations. All locks in the program are non-reentrant, i.e., if a thread holds a lock l, then it cannot re-acquire lock l without releasing it. If a thread is unable to acquire a lock, it blocks until the lock becomes available. The minimum value of x and the minimum value of y together for which execution of P can result in a deadlock are:

(A) x = 1, y = 2

(B) x = 2, y = 1

(D) x = 1, y = 1

Ans: (C)

48. The values of parameters for the Stop-and – Wait ARQ protocol are as given below:

Bit rate of the transmission channel = 1Mbps

Propagation delay from sender to receiver = 0.75 ms

Time to process a frame = 0.25ms

Number of bytes in the information frame =1980

Number of bytes in the acknowledge frame = 20

Number of overhead bytes in the information frame = 20

Assume that there are no transmission errors. Then the transmission efficiency ( expressed in percentage) of the Stop-and – Wait ARQ protocol for the above parameters is _________(correct to 2 decimal places)

Ans: (89.33)

49. A computer network uses polynomials over GF(2) for error checking with 8 bits as information bits and uses x³ + x + 1 as the generator polynomial to generate the check bits. In this network, the message 01011011 is transmitted as

(A) 01011011010

(B) 01011011011

(D) 01011011100

Ans: (C)

50. Let p, q, and r be propositions and the expression (p → q) → r be a contradiction. Then, the expression (r → p) → q is

(A) a tautology

(B) a contradiction

(D) always TRUE when q is TRUE

Ans: (D)

51. A cache memory unit with capacity of N words and block size of B words is to be designed. If it is designed as a direct mapped cache, the length of the TAG field is 10 bits. If the cache unit is now designed as a 16-way set-associative cache, the length of the TAG field is ______bits.

Ans: (14)

52. Consider the following two functions.

The output printed when fun1 (5) is called is

(A) 53423122233445

(B) 53423120112233

(D) 53423120213243

Ans: (A)

53. Consider a database that has the relation schema CR (Student Name, Course Name). An instance of the schema CR is as given below.

The following query is made on the database.

T1 → π_CourseName(σ_{StudentName = ‘SA’}(CR))

T2 ← CR ÷ T1

The number of rows in T2 is ____________.

Ans: (4)

54. Let A be n × n real valued square symmetric matrix of rank 2 with

Consider the following statements.

(I) One eigen value must be in [-5, 5]

(II) The eigen value with the largest magnitude must be strictly greater than 5.

Which of the above statements about eigen values of A is/are necessarily CORRECT?

(A) Both (I) and (II)

(B) (I) only

(D) Neither (I) nor (II)

Ans: (B)

55. Consider the context-free grammars over the alphabet {a,b,c} given below. S and T are nonterminals

G₁ : S → aSb|T, T→ cT|∈

G₂ :S → bSa|T, T → cT|∈.

The language L(G₁) ⋂ L(G₂) is

(A) Finite.

(B) Not finite but regular.

(D) Recursive but not context-free.

Ans: (B)

56. Research in the workplace reveals that people work for many reason ___________.

(A) money beside

(B) beside money

(D) besides money

Ans: (D)

57. After Rajendra chola returned from his voyage to Indonesia, he _______ to visit the temple in Thanjavur.

(A) was wishing

(B) is wishing

(D) had wished

Ans: (C)

58. Rahul Murali, Srinivas and Arul are seated around a square table. Rahul is sitting to the left of Murali. Srinivas is sitting to the right of Arul. Which of the following pairs are seated opposite each other ?

(A) Rahul and Murali

(B) Srinivas and Arul

(D) Srinivas and Rahul

Ans: (C)

59. Find the smallest number y such that y×162 is a perfect cube.

(A) 24

(B) 27

(D) 36

Ans: (D)

60. The probability that a k-digit number does NOT contain the digits 0,5,or 9 is

(A) 0.3^k

(B) 0.6^k

(D) 0.9^k

Ans: (C)

61. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this plot. If in a flood, the water level rises to 525m, which of villages P,Q, R, S,T get submerged ?

(A) P, Q

(B) P, Q, T

(D) Q, R, S

Ans: (C)

62. “The hold of the nationalist imagination on our colonial past is such that anything inadequately or improperly nationalist is just not history”

Which of the following statements best reflects the author’s opinion ?

(A) Nationalists are highly imaginative.

(B) History is viewed through the filter of nationalism.

(D) Nationalism has to be both adequately and properly imagined.

Ans: (B)

63. The expression is equal to

(A) the maximum of x and y

(B) the minimum of x and y

(D) None of the above

Ans: (B)

64. Six people are seated around a circular table. There are at least two men and two women . There are at least three right-handed persons. Every woman has a left-handed person to her immediate right. None of the women are right-handed. The number of women at the table is

(A) 2

(B) 3

(D) Cannot be determined

Ans: (A)

65. Arun, Gulab, Neel and Shweta must choose one shirt each from a pile of fours shirts coloured red, pink, blue and white respectively. Arun dislikes the colour red and Shweta dislikes the colour white. Gulab and Neel like all the colours. In how many different ways can they choose the shirts so that no one has a shirt with a colour he or she dislikes ?

(A) 21

(B) 18

(D) 14

Ans: (D)

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